How can x + 4 = 3x + 12 be set up as a system of equations?

To set up the equation x + 4 = 3x + 12 as a system of equations, we first need to rearrange this equation to express it in a standard form.

We start by moving all terms involving x to one side and constants to the other side. Here’s the step-by-step process:

1. Subtract x from both sides: 4 = 3x – x + 12
2. This simplifies to: 4 = 2x + 12

Next, we isolate the 2x term:

1. Subtract 12 from both sides: 4 – 12 = 2x

This results in:

-8 = 2x

Now, we can express this as an equation in the standard form:

2x + 8 = 0

Therefore, the original equation x + 4 = 3x + 12 can be set up as the following system of equations:

   2x + 8 = 0

If you want to represent this as two individual equations to create a system, you can introduce a new variable, say y:

   y = x + 4

   y = 3x + 12

So, the final system of equations looks like this:

   y = x + 4
   y = 3x + 12

This setup allows you to solve for both x and y simultaneously using methods like substitution or elimination.